Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done, if the group is to have a majority of boys?

Question

Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done, if the group is to have a majority of boys? (A)  120  (B)  80  (C)  90  (D)  100

Tardigrade Admin · Accepted Answer

The boys in majority, if boys are more than girls. The boys are in majority, if the groups are

4 B 3 G, 5 B 2 G, 6 B 1 G

.
Total number of combinations

=^{6} C_{4} \times^{4} C_{3} +^{6} C_{5} \times^{4} C_{2} +^{6} C_{6} \times^{4} C_{1}

= 15 \times 4 + 6 \times 6 + 1 \times 4

= 60 + 36 + 4 = 100

Q. Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done, if the group is to have a majority of boys?

$120$

$80$

$90$

$100$

Q. Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done, if the group is to have a majority of boys?

120

80

90

100

The boys in majority, if boys are more than girls. The boys are in majority, if the groups are 4B3G,5B2G,6B1G . Total number of combinations =6C4​×4C3​+6C5​×4C2​+6C6​×4C1​ =15×4+6×6+1×4 =60+36+4=100

Q. Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done, if the group is to have a majority of boys?

$120$

$80$

$90$

$100$